ページ1:

正弦定理: sinA
a
b
C
SinB
=
sin C
= 2R
前置:
:: sin A =
h
sin B
=
a
C
b
h = b sin A = a sin B -> ab
h
HA為銳角
2A= <D
BD =
2R,
sin D =
<BCD
C
a
R
B
sin A = 2
2R
a
A
a
=>
sinA
sinB
a
b
B
sin A
=
2R
a
C
#
b
=
同理可證:
sinA sin B sin C
=7
a
SinB
sin C
D
b
=
C
b
C
if ∠A為直角
sin A |
BC
=
= a = 2R
a
sin A
=
2R
#
C
b
a
2R
A
B
if A 為鈍角
ZA + 2D = 180
sin (180-A) sind
=> sin(180A) = sinA
a
.. Sin D = 2
a
=>
sinA
2R = SinA
= 2R
#
C
A
B
D
a
28

ページ2:

餘弦定理
c (bcos A, bsin A)
a
a² = BC = (c-bcos A)² + b² sin "A
=
c² 2cbcosA+ b² cos² A + b²sin²A
= b²(cos A+ sin ³ A) + C² - 2 cb cos A
=
|= |
b+c2bc coSA
=>
COSA
b² + c² - a²
=
2bc
h
=7
COSB
=
A
C
B
(0,0)
(c,o)
a² + c²-b²
2ac
2
a²+b²-c²
=7
cosC
=
2ab #